The present invention is directed to improving the stability of oscillators in applications such as communication systems which up or down convert signals in the transmitters and/or receivers and in frequency synthesizers where pure and stable frequency references are required. Other applications for the device and method of the present invention are in systems that require highly stable clock signals for reference purposes such as watches and computing devices and the device and method are also useful in any area where oscillators are applied. More particularly, the present invention is directed to concatenating a plurality of resonator/amplifiers in a loop to increase the effective quality and thereby the stability of the oscillator.
Any system in which timing is important in some way has a local oscillator and many systems also require accurate frequency references that are generated locally. For instance, radio would not be possible without a local oscillator in the transmitter and receiver for converting the information signals to the proper frequency bands. The performance of these systems is highly dependent on the stability of the frequency provided by the oscillator. Phase jitter (phase noise) in the output of the oscillator limits the accuracy of the reference and therefore limits the accuracy of the entire system. Amplitude variations in the output of the oscillator are important as well in many applications but these amplitude variations can be readily suppressed with a limiter or an automatic gain control.
The general structure for high performance oscillators include an amplifier which has its output fed back to its input via a resonating structure. The resonating structure produces a large output change when the frequency in the feedback loop varies and this output change opposes the frequency variations so that the frequency variations are minimized. As the change in the resonator output on a frequency variation becomes larger, the correction also becomes stronger. The resonator change with frequency is indicated by a quality or Q-value. A higher Q-value indicates that the resonator is more sensitive to frequency variations and therefore the ultimate oscillator output frequency will be more stable. In order to provide oscillators having pure and stable frequency outputs, low noise and high Q-values are required for the oscillator. High Q-values in the resonating structures for stable oscillators are essential because the final output spectrum of the oscillator is determined by the noise generated in the loop and the Q-value of the resonator.
FIG. 1 illustrates the configuration for a typical oscillator where an amplifier 10 is fed back by a passive, phase rotating network 20. The oscillator 5 starts to oscillate at the frequency for which the Barkhausen conditions are fulfilled where the loop gain is exactly 1 and the loop phase is 0 or a multiple of 2.pi.. The oscillator 5 is preferably designed such that the phase condition occurs in the steepest part in the phase characteristics of the resonator. More precisely, the Q-value of the network 20 is related to the phase derivative, or group delay .delta..phi./.delta..function. of the resonator according to: ##EQU1## where .function..sub.0 is the resonating frequency in Hz.
The output spectrum of the oscillator 5 can be determined by modeling the oscillator 5 as an extremely narrow band filter that filters the noise in the feedback loop. The noise power spectral density at the output S.sub.v, is thereby proportional to the white noise density S.sub.n in the loop and inversely proportional to Q.sup.2 of the resonating structure according to: ##EQU2## where v=.function./.function..sub.0 -.function..sub.0 /.function..
One technique for increasing the stability of an oscillator is to increase the effective Q-value by concatenating a plurality of passive, phase rotating networks. However, in practical use, the resonators used in the passive, phase rotating network 20 are either two-port or three-port devices which are generally not unilateral. Cascading these networks results in electrical interactions, and therefore does not result in an increase in the effective Q-value of the cascaded circuit. Resonators cannot simply be concatenated electrically in practical use due to the characteristics of the network. Therefore, it is desired to provide a means to cascade frequency selective circuits of an oscillator which prevents interaction and loading between the resonators.